In a book Conceptual Wavelets in Digital Signal Processing by Lee Fugal 2009 on page 246 the author talks about aliasing present in DWT subbands due to downsampling by 2 and states:
Recall from DSP that for a signal at 0.3 Nyquist aliasing from downsampling will "reflect" the signal across Nyquist. Thus we see the aliasing components at Nyquist minus 0.3 Nyquist or 0.7 Nyquist.
I thought it was safe to downsample a signal below 0.5 Nyquist by 2, isn't that correct ? Also on the image below the signal at 0.3 Nyquist and the alias at 0.7 Nyquist have different amplitudes.
I would think the aliasing in approximations can only occur because of imperfect filtering i.e. because some of the high frequencies above 0.5 Nyquist were also captured before downsampling by 2. But the author also shows using UDWT ( undecimated DWT ) with the same filters that without downsampling approximations after filtering have only frequencies around 0.3 Nyquist:
So where does aliasing come from in DWT in this example?